We propose a new transform speech codec that jointly encodes a wideband waveform and its corresponding wideband and narrowband speech recognition features. For distributed speech recognition, wideband features are compressed and transmitted as side information. The waveform is then encoded in a manner that exploits the information already captured by the speech features. Narrowband speech acoustic features can be synthesized at the server by applying a transformation to the decoded wideband features. An evaluation conducted on an in-car speech recognition task show that at 16 kbps our new system typically shows essentially no impact in word error rate compared to uncompressed audio, whereas the standard transform codec produces up to a 20% increase in word error rate. In addition, good quality speech is obtained for playback and transcription, with PESQ scores ranging from 3.2 to 3.4.